Differentiation will be used to find whether a function is increasing or decreasing.
Interval and nature of function
Theorem: Let f be continuous on [a, b] and differentiable on (a, b) Then:
- f is increasing in [a, b], if f’ (x) ≥ 0, ∀ x ∈ (a, b)
- f is decreasing in [a, b], if f’ (x) ≤ 0, ∀ x ∈ (a, b)
- f is a constant function in [a, b] if f’ (x) = 0, ∀ x ∈ (a, b)
Our R D sharma solutions for class 12 is beneficial for students who are in 12th standard and preparing for competitive examinations like Jee mains or advanced.
Increasing and Decreasing Functions Class 12th RD Sharma Exercises